Radioactive Decay Phosphorus:32 (P-32) has a hatufe of 14.2 days. IF 150 g of this substance are present initially, find the amount t) present after days. (ROL Q(t)- What amount (in grama) will be left after 25 6 days? (Round your answer to three decimal places.) How fast (in grams per day) is the P-32 decaying when t. 25,67 (Round your answer to three decimal places.) /day Need Help? With
Answers
The rate at which P-32 decays when t = 25.67 days is approximately 0.662 g/day (decay rate is negative as the amount is decreasing with time).
Given: Initial mass = 150 g, Half-life = 14.2 days,
Time = 25.67 days
Part (a) - Finding the amount present after 25.67 days
We know that the formula to find the amount of substance after time t is given by;
N(t) = N0 * (1/2)^(t/h)
Where,N0 is the initial amount of substance N(t) is the amount present after time t.
t is the time elapsedh is the half-life of the substance
Given, N0 = 150 g, h = 14.2 days,
t = 25.67 days∴ N(t) = 150 * (1/2)^(25.67/14.2)≈ 30.262 g
Hence, the amount of P-32 left after 25.67 days is approximately 30.262 g.
Part (b) - Finding the decay rate when t = 25.67 days
We know that the decay rate is given by; dN/dt = k * N
Where, k is the decay constant N is the amount of substance at time t We know that the relationship between half-life (h) and decay constant (k) is given by;
h = ln(2) / k∴ k = ln(2) / h = ln(2) / 14.2 days≈ 0.0489 / day
Given, t = 25.67 days and
N = 30.262 g dN/dt
= 0.0489 * 30.262 * (1/2)^(25.67/14.2)≈ -0.662 g / day.
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Related Questions
Let A={(x-3)/(x-2)ЄR : X<0}
be a subset of real numbers.
i) Define A's supremum and infimum.
Answers
The supremum of the set A does not exist (it is negative infinity), and the infimum of the set A is 1.
To define the supremum and infimum of the set A, we first need to determine the properties of the set.
The set A is defined as A = {(x-3)/(x-2) ∈ R : x < 0}.
To find the supremum (also known as the least upper bound) of A, we need to find the smallest value that is greater than or equal to all the elements of A. In other words, we are looking for the least upper bound of the set A.
Let's analyze the elements of A:
For x < 0, the expression (x-3)/(x-2) can take on different values depending on the value of x. We need to find the maximum value that this expression can reach for all x < 0.
As x approaches 0 from the left side, (x-3)/(x-2) approaches negative infinity. Therefore, there is no finite supremum for the set A.
Next, let's find the infimum (also known as the greatest lower bound) of A. We need to find the largest value that is less than or equal to all the elements of A. In other words, we are looking for the greatest lower bound of the set A.
Again, analyzing the elements of A:
As x approaches negative infinity, (x-3)/(x-2) approaches 1. Therefore, the infimum of the set A is 1.
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the following table provides a probability distribution for the random variable . 2 0.20 4 0.30 7 0.40 9 0.10 a. compute (to 1 decimal). b. compute and (to 2 decimals).
Answers
The value of Expected value, variance, and standard deviation of y of given probability distribution is 6.4, 9.76 and 3.12 respectively.
To compute the expected value of y, denoted E(y), we use the formula:
E(y) = Σ [y × f(y)]
Using the given probability distribution, we have:
E(y) = (2 × 0.20) + (4 × 0.30) + (7 × 0.40) + (8 × 0.10) = 1.6 + 1.2 + 2.8 + 0.8 = 6.4
Therefore, the expected value of y is 6.4, rounded to 1 decimal place.
To compute the variance of y, denoted Var(y), we use the formula:
Var(y) = E(y^2) - [E(y)]^2
where E(y) is the expected value of y, and E(y^2) is the expected value of y squared. To find E(y^2), we use the formula:
E(y^2) = Σ [y^2 × f(y)]
Using the given probability distribution:
E(y^2) = (2^2 × 0.20) + (4^2 × 0.30) + (7^2 × 0.40) + (8^2 × 0.10) = 1.6 + 3.6 + 19.6 + 6.4 = 31.2
Substituting this and the previously calculated E(y) into the formula for Var(y), we get:
Var(y) = E(y^2) - [E(y)]^2 = 31.2 - 6.4^2 = 31.2 - 40.96 = 9.76
Therefore, the variance of y is 9.76, rounded to 2 decimal places.
we take the square root of the variance to find the standard deviation:
σ = √Var(y) = √9.76 = 3.12
Therefore, the standard deviation of y is 3.12, rounded to 2 decimal places.
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____The given question is incomplete, the complete question is given below:
The following table provides a probability distribution for the random variable y 2 4 7 f(u) 0.20 0.30 0.40 0.10 8 a. Compute E(y) (to 1 decimal). 5.2 b. Compute Var(y) and ơ (to 2 decimals). Var(y)
The points B(2,-8), C(2, 1), D(-3, 5), and E(-3,-4) form parallelogram BCDE.
Plot the points then click the "Graph Quadrilateral" button. Then find the perimeter
of the parallelogram. Round your answer to the nearest tenth if necessary
Answers
The perimeter of parallelogram BCDE is 38 .
The distance between two points is the length of the line segment connecting the two points. The distance between two points on the xy plane can be found using the distance formula. The ordered pair (x,y) represents the coordinates of the point, where the x-coordinate (or abscissa) is the distance from the x-axis to the point, and the y-coordinate (or ordinate) is the distance to the point. from the y-axis which is given by \(Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\) where \((x_1 , y_1)\) is the coordinate of first point and \((x_2 , y_2)\) is the coordinate of second point .A shape's perimeter is defined as the total length of its bounds. The perimeter of a shape is determined by summing all sides and side lengths that enclose the shape.The plotting of the points B(2,-8), C(2, 1), D(-3, 5), and E(-3,-4) is given below.
Using distance formula , put \(x_1=2, \ y_1 =-8\) and \(x_2=2, \ y_2 =1\) in equation (1) , we get BC
\(BC=\sqrt{(2-2)^2+(1-(-8))^2} \\BC=\sqrt{0+(1+8)^2} \\BC=\sqrt{(9)^2} \\BC= 9\)
Using distance formula , put \(x_1=2, \ y_1 =1\) and \(x_2=-3, \ y_2 =5\) in equation (1) ,we get CD
\(CD=\sqrt{(-3-2)^2+(5-1)^2} \\CD=\sqrt{(-5)^2+(4)^2} \\CD=\sqrt{25+16} \\CD=\sqrt{100} \\CD=10\)
Using distance formula , put \(x_1=-3, \ y_1 =5\) and \(x_2=-3, \ y_2 =-4\) in equation (1) ,we get DE
\(DE=\sqrt{(-3-(-3))^2+(-4-5)^2} \\DE=\sqrt{(-3+3)^2+(-9)^2} \\DE=\sqrt{0+81} \\DE=\sqrt{81} \\DE=9\)
Using distance formula , put \(x_1=2, \ y_1 =-8\) and \(x_2=-3, \ y_2 =-4\) in equation (1) ,we get BE
\(BE=\sqrt{(-3-2)^2+(-4-(-8))^2} \\BE=\sqrt{(-5)^2+(-4+8)^2} \\BE=\sqrt{25+(4)^2} \\BE=\sqrt{25+16} \\BE=\sqrt{100} \\BE=10\)
Perimeter \(=10+10+9+9=38\)
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I need it as a linear function thank you
Answers
\(5~~,~~\stackrel{5(6)}{30}~~,~~\stackrel{30(6)}{180}~~,~~\stackrel{180(6)}{1080}~~,~~\stackrel{1080(6)}{6480}~\hfill \boxed{f(x)=x_{n-1}(6)}\)
now, that's recursive, we can also write it in explicit as \(5(6)^x\)
Data were recorded for a car’s fuel efficiency, in miles per gallon (mpg), and corresponding speed, in miles per hour (mph). given the least-squares regression line, , what is the fuel efficiency for a speed of 60 mph? 3.65 mpg 33.90 mpg 36.52 mpg 38.55 mpg
Answers
The least-square regression line between data fuel efficiency and speed is In(Fuel Efficiency) = 1.437 + 0.541 In(Speed). The fuel efficiency when the speed 60 mph is 38.55 mpg
Least square regression is a representation of data in a linear equation:
y = ax + b
where x, y are data variables.
The least-squares regression line is obtained by minimizing the distance from regression line to each data points.
In the given problem, the given least-squares regression line is:
In(Fuel Efficiency) = 1.437 + 0.541 In(Speed)
In this case,
y = In(Fuel Efficiency)
x = ln(Speed)
Where ln is the natural logarithmic operator.
When speed = 60 mph, then,
In(Fuel Efficiency) = 1.437 + 0.541 In(60)
In(Fuel Efficiency) = 1.437 + 2.215
In(Fuel Efficiency) = 3.65
Fuel efficiency = e^(3.65) = 38.55
Hence, the fuel efficiency when the speed 60 mph is 38.55 mpg
Your question is incomplete, but most probably your question was:
Data were recorded for a car's fuel efficiency, in miles per gallon (mpg), and corresponding speed, in miles per hour (mph). Given the least-squares regression line, In(Fuel Efficiency) = 1.437 + 0.541 In(Speed), what is the fuel efficiency for a speed of 60 mph? 3.65 mpg 33.90 mpg 36.52 mpg 38.55 mpg
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anyone know what -36 divide by 4 is i forgot lol
Answers
write an equation for the nth term of the geometric sequence 896, -448, 224... find the 8th term of this sequence.
Answers
Answer:
-7
Step-by-step explanation:
nth term of a geometric sequence is given by ar^(n-1),
where a is first term, r is the common ratio.
a = 896. ratio = -448/896 = - 0.5.
8th term = (896) (-0.5)^(8-1)
= (896) (-0.5)^7
= -7
How do you know that there rational
Answers
we can conclude that the sum of (-2+3÷4) and 5÷g is rational, The sum is not necessarily an integer, since it could be a fraction.
Why it is?
To determine if the sum of (-2 + 3÷4) and 5÷g is rational, we need to first simplify the expression:
(-2 + 3÷4) + 5÷g = (-8÷4 + 3÷4) + 5÷g = -5/4 + 5÷g
Now, we can see that the sum is rational if -5÷4 and 5÷g are both rational.
-5÷4 is rational because it can be expressed as a fraction (-5÷4 = -1.25).
For 5÷g to be rational, g must be a non-zero rational number, because the product of a rational number and a non-zero rational number is always rational.
Therefore, we can conclude that the sum of (-2+3÷4) and 5÷g is rational.
The sum is not necessarily an integer, since it could be a fraction.
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Add both numbers first which gives value -79/36.which is a rational number
Step-by-step explanation:
What is a rational number ?
A number which can be represented as p/q , where P and Q are integers and q is not equal to 0.
By which symbol set of rational numbers is expressed?
Set of rational numbers is expressed by Q.
So, to know that given numb is rational or not we will check that it can be written in P/q form or not after verifying it we will check that p and q are integers or not , after that check if q is not 0.
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Antwaun wants to set aside 12% of his budget towards food. If his net pay* is $4,000, how
would you set up the equation?
Answers
Answer:
Amount set aside for food = 0.12 × 4,000
Step-by-step explanation:
His net pay = $4,000
His budget
Food = 12% of his budget
Assume $4,000 is his budget
Then,
Food = 12% of $4,000
= 12/100 × 4,000
= $480
The Equation is
Amount set aside for food = 0.12 × 4,000
The equation would be set up as follows:
\(\begin{aligned} \rm {Amount \: for \: food \: pay} &= \dfrac{12 \times 4000}{100}\\&= \$\:480 \end{aligned}\)
Given that:
Amount of net pay is $4,000
Percentage of budget used for food is 12%
To calculate the amount towards food, we'll take out 12% of amount of net pay which is $4,000.
It would be written symbolically as:
\(\begin{aligned} \rm {Amount \: for \: food \: pay} &= \dfrac{12 \times 4000}{100}\\&= \$\:480 \end{aligned}\)
Thus, amount for food pay is in total $ 480, and is calculated by above equation.
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for the following data set, calculate the pearson correlation. x y 2 6 1 2 3 4 a. 0.5 b. 0.25 c. –0.25 d. –0.5
Answers
The Pearson correlation coefficient for the given data set is 0.5 (option a).
To calculate the Pearson correlation coefficient,
1: Calculate the mean of x and y.
Mean of x: (2 + 1 + 3) / 3 = 2
Mean of y: (6 + 2 + 4) / 3 = 4
2: Calculate the deviation of each value from the mean for both x and y.
x deviation: (2 - 2), (1 - 2), (3 - 2) = 0, -1, 1
y deviation: (6 - 4), (2 - 4), (4 - 4) = 2, -2, 0
3: Calculate the product of the deviations for each pair of values.
Product of deviations: (0 * 2), (-1 * -2), (1 * 0) = 0, 2, 0
4: Calculate the squared deviation for each value of x.
x squared deviation: \((0^2), (-1^2), (1^2)\) = 0, 1, 1
5: Calculate the squared deviation for each value of y.
y squared deviation: \((2^2), (-2^2), (0^2)\) = 4, 4, 0
6: Sum up the products of the deviations and divide by the square root of the product of the squared deviations of x and y.
Pearson correlation coefficient: (0 + 2 + 0) / sqrt((0 + 1 + 1) * (4 + 4 + 0))
Pearson correlation coefficient: 2 / sqrt(2 * 8)
Pearson correlation coefficient: 2 / sqrt(16)
Pearson correlation coefficient: 2 / 4
Pearson correlation coefficient: 0.5
Therefore, the Pearson correlation coefficient for the given data set is 0.5, which corresponds to option a.
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3(x-2) + 1 = 2(x-4) + x + 13
Answers
3(x - 2) + 1 = 2(x - 4) + x + 13
3x - 6 + 1 = 2x - 8 + x + 13
3x + 7 = 3x + 5
3x + 7 = 3x + 5
-5 -5
----------------------
3x + 2 = 3x
-3x -3x
-----------------
2
Because there is no x, there is no solution
i need help with this one?
Answers
The best description of the transformation for the image being projected on the retina is A. A dilation with a scale factor between 0 and - 1 and center at the nodal point.
How does the nodal point dilate the retina ?An mage is inverted and reversed as it passes through the lens of the eye, and is then projected upside down and reversed onto the retina. The process of transforming the image is called "rectification."
In mathematical terms, a dilation would have taken place because the object was shrunken by the eyes at the nodal point. When an object shrinks , then the scale factor is between 0 and 1 but because this image is inverted, the scale factor is between 0 and - 1.
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Jordan is saving for a new laptop that costs $325. He uses the equation and table below to show the number of months he has been saving, m, and the total amount he has saved so far, d. d=80+ 75m Amount Saved Over Several Months Months (m) Total Saved in Dollars (d) 0 1 Which is the first month in which Jordan will have saved enough money to buy the laptop? Month 2 O Month 3 O Month 4 month 5
Answers
Answer:
month 4
Step-by-step explanation:
I took the test
Answer:
Its month 4 on edge.
Step-by-step explanation:
HELP ME PLS
A media research survey showed that one evening, 2/3 of all U.S. households had their televisions on, and 3/8 of them were watching a World Series baseball game. What fraction of the U.S. households was watching the game?
Answers
Answer:
sfhjty
Step-by-step explanation:
Construct validity ensures that the measure includes an adequate and representative set of items. A) True B) False
Answers
Answer:
false
Step-by-step explanation:
The statement "Construct validity ensures that the measure includes an adequate and representative set of items." is true because researchers can determine the extent to which a measure has construct validity and whether it includes an adequate and representative set of items.
Construct validity is established by accumulating evidence through various means. One way to establish construct validity is by examining the content of the measurement tool. This involves carefully selecting items that represent the construct of interest.
In mathematical terms, we can think of construct validity as a process of creating a mathematical model that accurately reflects the construct being measured. This model should include a comprehensive set of items that adequately represent the construct.
In practice, researchers employ statistical techniques such as factor analysis to examine the relationships between the items and the construct.
Construct validity also involves assessing the convergent and discriminant validity of the measure. Convergent validity refers to the degree to which different items measuring the same construct are positively related to each other.
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Enter the correct answer in the box. Consider the graph of the sixth-degree polynomial function f. Replace the values b, c, and d to write function f.
f(x)=(x-b)(x-c)^2(x-d)^3
Answers
Answer: (x - 1)(x + 1)^2(x - 4)^3
Step-by-step explanation:
First, remember that:
in expressions like: (x - b)^n
b is the value of x where the graph intersects the x-axis.
n can represent:
n = 1, the line just goes through the x-axis
n = 2, the line may change the direction (an inflection point), and touch the x-axis in one point.
n = 3, the line may have two inflection points when it intersects the x-axis.
Then we have the expression:
(x-b)(x-c)^2(x-d)^3
b is in the linear part, the graph crosses the x-axis linearly in x = 1.
c is in the quadratic part, the graph crosses the x-axis with one point of inflection at x = -1.
d is in the cubic part, the graph crosses the x-axis with two inflections in x = 4.
Then we can writhe the polynomial as:
f(x) = (x-1)(x-(-1))^2(x-4)^3 = (x - 1)(x + 1)^2(x - 4)^3
Answer:
(x - 1)(x + 1)^2(x - 4)^3
find the equation of the linethe line passes through the points (5,2) and (-4,-4)
Answers
Answer:
\(y = \frac{2}{3}x - \frac{4}{3} \)
Step-by-step explanation:
first find the slope using the above points then use the slope formula to calculate the slope
\(m = \frac{y2 - y1}{x2 - x1} \\ \frac{2 - - 4}{5 - - 4} = \frac{2 + 4}{5 + 4} = \frac{6}{9} = \frac{2}{3} \)
substitute ⅔ for m and one of the above points into the y-intercept form of the equation for a line and solve for b
\(y = mx + b \\ 2 = \frac{2}{3} (5) + b \\ 2 = \frac{10}{3} + b \\ 2 - \frac{10}{3} = b \\ \frac{6}{3} - \frac{10}{3} = b \\ b = - \frac{4}{3} \)
substitute the slope and the value for b into the equation to get the answer
\(y = \frac{2}{3} x - \frac{4}{3} \)
Is (-1, -4) a solution to a equation y=6x_ -2?
Answers
Write in slope-intercept form an equation of the line that passes through the given points.
(−2, 3), (2, 7)
Answers
Slope intercept form is y=mx+b.
m (the slope) is 4/4 which is equal to 1
b (the y intercept) is when x is zero meaning that it would be 5
Insert these into the equation:
y=1x + 5
1 x is equal to x so it can be simplified to
y= x + 5
The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
The equation of the line is y = x + 5
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The equation of a line y = mx + c
Now,
The equation of the line passes through the points:
(-2, 3) and (2, 7).
This means,
(-2, 3) = (a, b)
(2, 7) = (c, d)
The slope is given as:
Slope:
= (d - b) / (c - a)
= (7 - 3) / (2 + 2)
= 4 / 4
= 1
Now,
The line passes through point (-2, 3) = (x, y) so,
3 = (-2) x 1 + c
3 = -2 + c
c = 3 + 2
c = 5
Now,
m = 1
c = 5
The equation of the line is y = x + 5
Thus,
The equation of the line is y = x + 5
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Cookie come in
package of 9. Sarah ate
78 cookie. How many
whole boxe did he eat?
How many cookie doe
he have left?
Answers
Sarah ate 8 boxes of cookies and has 6 cookies left.
There are four basic arithmetic operations in mathematics: addition, subtraction, multiplication, and division. Among these four procedures, division is one of the most important in our everyday tasks. It is the division of a large group into equal smaller groups.
Division is one of the four fundamental mathematical operations, along with addition, subtraction, and multiplication. Division is described as the separating of a big group into smaller groups so that each group has an equal number of things. In mathematics, it is an operation used for equal grouping and equal sharing.
We can use division to find the number of boxes Sarah ate and the number of cookies she has left.
To find the number of boxes Sarah ate:
78 cookies ÷ 9 cookies per box
= 8.67 boxes (rounded down to the nearest whole number, 8 boxes)
To find the number of cookies Sarah has left:
78 cookies - 8 boxes x 9 cookies per box
= 78 cookies - 72 cookies
= 6 cookies
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What is the value of x?
Triangle V P M. Angle V is 47 degrees, angle P is 85 degrees, and angle M is x degrees.
degrees
Answers
Answer:
48
Step-by-step explanation:
I know I'm super late, so so sorry but for another in the future, it's 48
Answer:
48
Step-by-step explanation:
7. A Jar contains 26 marbles. It has 10 red, 8 black and 8 green marbles. Two marbles are drawn, the first is not returned before the second one is drawn. What is the probability thatboth marbles are green?OP(Both Green) -OP(Both Green) -OP(Both Green) -OP(Both Green) - 1
Answers
Given:
The total number of marbles are 26.
Red marbles=10
Black marbles=8
Green marbles=8
The two marbles are drawn randomly,
To find the probability that both marbles are green,
The probability that first marbles chosen is green,
\(\begin{gathered} P=\frac{desired\text{ outcomes}}{\text{Total outcomes}} \\ P=\frac{8}{26} \end{gathered}\)Condition is given that the first is not returned before the second one is drawn.
Now the we have 7 green marbles and total marbles are 25.
Probability is given by,
\(P=\frac{7}{25}\)The total probability of getting both green marbles without replacement is,
\(\begin{gathered} P=\frac{8}{26}\times\frac{7}{25} \\ P=\frac{4}{13}\times\frac{7}{25} \\ P=0.08615 \end{gathered}\)Answer: Probability is 0.08615.
2. Let f(x) = 3x² -x+5, find f(x+1)
Answers
Answer:
f(x + 1) = 3x² + 5x + 7
Step-by-step explanation:
To find f(x + 1), substitute x = x + 1 into f(x), that is
f(x + 1) = 3(x + 1)² - (x + 1) + 5 ← expand (x + 1)² using FOIL
= 3(x² + 2x + 1) - x - 1 + 5 ← distribute parenthesis by 3
= 3x² + 6x + 3 - x - 1 + 5 ← collect like terms
= 3x² + 5x + 7
3/2(4x-1)-3x5/4 -(x-+2)
Answers
Please mark brainliest
Solve for x: 3 < x + 3 < 6
Answers
Hey there!
\(Answer:\boxed{0<x<3}\)
\(Explanation:\)
Graph below!
Hope this helps!
\(\text{-TestedHyperr}\)
At 5:00 pm Antonio turned off the oven
Answers
Answer:
Or did he?
Step-by-step explanation:
Your first job as a new engineer is to estimate the cost of a new 3000−ft
2
heat exchange system for a plant retrofit. Your company paid $75,000 for a 1200- ft
2
heat exchanger 7 years ago. After a quick check in the literature, you determine the price index 7 years ago was 1360 and is 1478 today. If the power-sizing exponent is 0.55, determine a rough estimate for the cost of the new heat exchanger system.
Answers
The estimated cost of the new 3000-ft2 heat exchange system for the plant retrofit can be calculated using the power-sizing exponent and the price index. Based on the given information, the rough estimate for the cost of the new heat exchanger system is approximately $108,984.
To estimate the cost of the new heat exchange system, we need to consider the price index and the power-sizing exponent. The price index provides a measure of the change in prices over time. In this case, the price index 7 years ago was 1360, and the current price index is 1478.
To calculate the cost estimate, we can use the following formula:
Cost estimate = (Cost of previous heat exchanger) × (Current price index / Previous price index) × (New size / Previous size) ^ power-sizing exponent
Using the given information, the cost of the previous heat exchanger was $75,000, the previous size was 1200 ft2, and the new size is 3000 ft2.
Plugging in these values into the formula, we get:
Cost estimate = ($75,000) × (1478 / 1360) × (3000 / 1200) ^ 0.55
Simplifying the calculation, we find:
Cost estimate ≈ $108,984
Therefore, a rough estimate for the cost of the new 3000-ft2 heat exchanger system for the plant retrofit is approximately $108,984. It's important to note that this is just an estimate and the actual cost may vary based on specific factors and market conditions.
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HELP ME IM A 6TH
GRADER
Answers
Answer:
Its B, C, and D
Step-by-step explanation:
Find the slope (4,-1) (-2,6)
Answers
Answer:
7/-6
Step-by-step explanation:
y2-y1/x2-x1
6--1/-2-4
6+1/-2-4
7/-6
Hope This Helps!!
find the tangential and normal components of the acceleration vector. r(t) = 5(3t − t3) i 15t2 j
Answers
The tangential component of the acceleration vector is given by the derivative of the velocity vector with respect to time, which is the second derivative of the position vector with respect to time.
In this case, the tangential component is obtained by taking the derivative of the velocity vector r'(t) = (5(3 − 3t^2))i + (30t)j. The normal component of the acceleration vector is obtained by taking the magnitude of the acceleration vector and subtracting the tangential component.
It represents the acceleration perpendicular to the tangent line. The magnitude of the acceleration vector is given by |a(t)| = sqrt((5(−6t))² + (30)²) = 30sqrt(t² + 1), and the normal component can be calculated as sqrt((5(−6t))² + (30)²) - |r''(t)|.
Learn more about acceleration here:- brainly.com/question/2303856
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